Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Rumpf, Raymond C.

doi:10.2528/pierb11083107

Cited by 136 publications

(115 citation statements)

References 41 publications

(55 reference statements)

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“…Instead, we eliminate the z components of the fields, as, for example, done in [11,12], to obtain a reduced problem of dimension four. We first introduce block-matrices:…”

Section: The Wave Vector Eigenvalue Equationmentioning

confidence: 99%

“…We now reduce Equation (12) for all other cases l ‰ 0 for which the first term vanishes trivially. The integral in the second term is in the first reduction step written as a sum over the triangles o τ using the scaled lattice vector s l " l{p2πı l¨lq:…”

Section: Fourier Integralsmentioning

confidence: 99%

“…The scattering matrix for a finite slab is obtained by the Redheffer star product (Equation (22) in [12]) between both interfacial scattering matrices (no phase matrix as in the generalized Airy formulae [41] are necessary due to the global choice of origin for S l and S r . ): …”

Section: )mentioning

confidence: 99%

“…While the bulk modes themselves can be extracted to high accuracy from, e.g., finite element method (FEM) calculations (cf. [7,8]), the scattering problem itself is conveniently solved in Fourier space using Floquet's theorem and the orthogonality of plane waves [9][10][11][12]. Hence, the accuracy is lost laterally as a result of the numerical Fourier cutoff.…”

Section: Introductionmentioning

confidence: 99%

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Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

Saba

Schröder‐Turk

2015

Crystals

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We propose a new approach to calculate the complex photonic band structure, both purely dispersive and evanescent Bloch modes of a finite range, of arbitrary three-dimensional photonic crystals. Our method, based on a well-established plane wave expansion and the weak form solution of Maxwell's equations, computes the Fourier components of periodic structures composed of distinct homogeneous material domains from a triangulated mesh representation of the inter-material interfaces; this allows substantially more accurate representations of the geometry of complex photonic crystals than the conventional representation by a cubic voxel grid. Our method works for general two-phase composite materials, consisting of bi-anisotropic materials with tensor-valued dielectric and magnetic permittivities ε and µ and coupling matrices ζ. We demonstrate for the Bragg mirror and a simple cubic crystal closely related to the Kelvin foam that relatively small numbers of Fourier components are sufficient to yield good convergence of the eigenvalues, making this method viable, despite its computational complexity. As an application, we use the single gyroid crystal to demonstrate that the consideration of both conventional and evanescent Bloch modes is necessary to predict the key features of the reflectance spectrum by analysis of the band structure, in particular for light incident along the cubic [111] direction.

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“…Instead, we eliminate the z components of the fields, as, for example, done in [11,12], to obtain a reduced problem of dimension four. We first introduce block-matrices:…”

Section: The Wave Vector Eigenvalue Equationmentioning

confidence: 99%

Section: Fourier Integralsmentioning

confidence: 99%

Section: )mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

Saba

Schröder‐Turk

2015

Crystals

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“…In addition to controlling the amplitude reflectance, the wave also acquires a phase shift. Both the reflectivity and phase shift can be calculated using finite element method simulations with Floquet boundary conditions or rigorous coupled wave analysis (RCWA) [20,21], which can give modes and reflection properties at the same time.…”

Section: Design Approachmentioning

confidence: 99%

Integrated optical force sensors using focusing photonic crystal arrays

Guo¹,

Norte²,

Gröblacher³

2017

Opt. Express

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Mechanical oscillators are at the heart of many sensor applications. Recently several groups have developed oscillators that are probed optically, fabricated from high-stress silicon nitride films. They exhibit outstanding force sensitivities of a few aN/Hz 1/2 and can also be made highly reflective, for efficient detection. The optical read-out usually requires complex experimental setups, including positioning stages and bulky cavities, making them impractical for real applications. In this paper we propose a novel way of building fully integrated all-optical force sensors based on low-loss silicon nitride mechanical resonators with a photonic crystal reflector. We can circumvent previous limitations in stability and complexity by simulating a suspended focusing photonic crystal, purely made of silicon nitride. Our design allows for an all integrated sensor, built out of a single block that integrates a full Fabry-Pérot cavity, without the need for assembly or alignment. The presented simulations will allow for a radical simplification of sensors based on high-Q silicon nitride membranes. Our results comprise, to the best of our knowledge, the first simulations of a focusing mirror made from a mechanically suspended flat membrane with subwavelength thickness. Cavity lengths between a few hundred µm and mm should be directly realizable.

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An Ultrathin Transparent Radiative Cooling Photonic Structure with a High NIR Reflection

Dang

Wang

2022

Adv Materials Inter

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What's more, to make the DPRC devices economical and manufactured in large scale, polymers and microspheres are applied. [15,[19][20][21][22] General DPRC applications should selectively emit thermal radiation in the atmospheric window and minimize solar absorption, simultaneously. However, for transparent applications (e.g., transparent electrode, [23,24] display device, [25][26][27] and window [28][29][30][31] ), only visible light (0.38-0.78 µm) is allowed for view or illumination. The rest of the solar radiation (mainly NIR: 0.78-2.5 µm), if transmitted will cause overheating or additional energy for cooling.Many transparent NIR filters are proposed to block the NIR solar radiation in recent years. [27][28][29][30][31][32][33][34][35][36][37][38][39][40][41] However, several NIR filters block the NIR solar radiation by absorption, [28][29][30][31][32][33][34][35][36] for example, W 18 O 49 , [28] Cu 2−x S/SiO 2 [29] and (NH4) x WO 3 , [32] which will increase the additional heating load as well. [33] To reduce the heating load, it is important to filter the NIR solar radiation by reflection. [33][34][35][36][37][38][39][40][41] Such NIR reflecting filters can be realized by a conductive layer, [33][34][35][36][37][38][39][40][41] for example, ITO [37,40] and dielectric/metal/ dielectric (D/M/D) structure. [38,39,41] However, these NIR reflecting filters will also show high reflections (low emissions) within mid-infrared (MIR) bands, which suppress the radiative cooling. [37][38][39][40][41][42][43][44] As the radiative cooling power in 8-13 µm is significant, [1][2][3][4][5][6] the MIR radiation heat transfer between the cold sky and a NIR filter shouldn't be neglected. To realize high visible transmission, NIR reflection and MIR emission, simultaneously, one can combine a NIR reflecting filter (e. g., D/M/D [38][39][40][41][42][43][44] or ITO [37] ) and a transparent MIR emitting structure (e. g., SiO 2 [45,46] or PDMS [37,47] ). As a common visible transparent NIR reflecting film in energy saving, a D/M/D structure is often used as a spectrally selective filter that can transmit most of the visible light and reflect NIR solar radiation. [38][39][40][41][42][43][44][45][46] Dielectric layers can enhance visible transmission due to a destructive multi-reflective interference and a thin metal layer is responsible for NIR reflection, [38][39][40][41][42][43][44][45] which is higher than that of an ITO structure. [38] As a polymer, PDMS will age especially under sunlight [48,49] and it is much thicker than a SiO 2 based emitter. [45,46] As a potential material for transparent radiative cooling, silica is stable with high transmittance over most of the solar wavelength range and also exhibits a strong phononpolariton resonance in the wavelength range of 8-13 µm. [45,46] However, there is an emission dip within 8-13 µm for a silica layer. [45] With 2D silica photonic crystals [45] or gratings, [46] silica can show enhanced MIR emission. As a result, it is expected With a high NIR reflection, a transparent radiativ...

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Improved Formulation of Scattering Matrices for Semi-Analytical Methods That Is Consistent With Convention

Cited by 136 publications

References 41 publications

Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

Bloch Modes and Evanescent Modes of Photonic Crystals: Weak Form Solutions Based on Accurate Interface Triangulation

Integrated optical force sensors using focusing photonic crystal arrays

An Ultrathin Transparent Radiative Cooling Photonic Structure with a High NIR Reflection

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